CN109765249A - A kind of CT system parameter calibration and imaging method based on random transformation - Google Patents
A kind of CT system parameter calibration and imaging method based on random transformation Download PDFInfo
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Abstract
Present invention relates particularly to a kind of CT system parameter calibrations and imaging method based on random transformation, the calibrating template of two homogeneous solid media composition is placed on square pallet, known to the geological information and absorptivity of template, according to the calibrating template and its information is received, solves position, the spacing of detector cells and 180 directions of X-ray of the CT system rotation center in square pallet；The reception information for the unknown medium 1 that CT system obtains in Utilizing question 1, the corresponding data file of unknown medium 1 determine position, geometry and the absorptivity of the unknown medium 1 in square pallet it is known that calibrating parameters in Utilizing question 1；It is similarly obtained the relevant information of unknown medium 2；Design new template establishes corresponding peg model, to improve the stated accuracy and stability of CT system.The method increase the precision of parameter, and image quality is high, and it is intuitive and easy to understand to solve parameters method.
Description
Technical field
The invention belongs to CT technical applications, and in particular to a kind of CT system parameter calibration based on random transformation
With imaging method.
Background technique
CT technology reconstructs object faultage image using the dampening information that X-ray penetrates object.Now consider a two-dimensional ct
System: in detector plane vertical direction, X-ray is incident in parallel, 512 detector cells equidistant arrangements of the detector.Gu
The position of fixed two dimension detected medium, the rotation center for allowing entire emitting-receiving system to fix around certain rotate 180 times counterclockwise,
In other words, X-ray direction changes 180 times.Ray energy after two-dimentional detected medium attenuation by absorption can measure, by gain
Deng processing after obtain 180 groups of reception information.In order to improve image quality, the parameter of CT system is often demarcated by means of template,
And the sample of unknown structure can be imaged accordingly.
Summary of the invention
In order to solve the problems, such as that image quality existing in the prior art is not good enough, the present invention provides one kind to be based on random
The CT system parameter calibration and imaging method of transformation.The technical problem to be solved in the present invention is achieved through the following technical solutions:
A kind of CT system parameter calibration and imaging method based on random transformation, comprising:
Problem 1, the calibrating template that two homogeneous solid media composition is placed on square pallet, the geological information of template
With absorptivity it is known that according to the calibrating template and its receiving information, position of the CT system rotation center in square pallet is solved
It sets, 180 directions of the spacing of detector cells and X-ray；
The reception information for the unknown medium 1 that CT system obtains in problem 2, Utilizing question 1, the corresponding data of unknown medium 1
File determines position of the unknown medium 1 in square pallet, geometry it is known that calibrating parameters in Utilizing question 1
And absorptivity；
The reception information for another unknown medium 2 that CT system obtains in problem 3, Utilizing question 1, unknown medium 2 are corresponding
Data file it is known that calibrating parameters in Utilizing question 1, provide position of the unknown medium 2 in square pallet, geometry
Shape and absorptivity；
Problem 4, design new template establish corresponding peg model, to improve the stated accuracy and stability of CT system.
Further, the specific method is as follows for the parameter calibration of above-mentioned CT system:
When testee is uniform dielectric, the transmitted intensity across object is exponentially decayed, it then follows
Lambert-beer law, being formulated out is exactly w=w0e-αl；
And on the path that ray only passes through air, the intensity of X-ray is almost unchanged, and therefore, the value of air is almost
It is zero；
In x-y plane, if the distribution function of attenuation coefficient is p (x, y), in the ray where l on the direction of straight line
Strength Changes are
After taking negative logarithm, it is denoted as f, physical quantity can be surveyed by being one, its physical significance is substance under the energy-ray
Line integral of the attenuation coefficient on the direction straight line l,
∫lP (x, y) dl=α ln (w/w0)
Due to homogeneous media in this subject, distribution function p (x, y) permanent is definite value.
Further, the determination method of the position of above-mentioned unknown medium 1, geometry and absorptivity is as follows:
CT, which is imaged, is equivalent to the projection value Rg (t, θ) detected to all, the function g (x, y) of reverse attenuation coefficient,
This refutation process can by Radon transform,
The parametric form definition of Radon transform is
Wherein g (x, y) function any straight line xcos θ+ysin θ=t in plane can be accumulated, above formula be known as function g (x,
Y) Radon transform is remembered b (t, θ)=Rg (t, θ)；
The gain coefficient of CT system is first found out, gain then is carried out to data
Wherein α=ln [(l0- l) l], calculate α=1.75；
Since the rotation center of CT system is not or not the center of square pallet, it is therefore desirable to do translation variation ability to data
Restore the raw information of data；
If rotation center is (a, b), following translation variation is done,
R ρ (t, θ)=Rf (t-acos θ-bsin θ, θ)
Known by Central slice theorem, image reconstruction is exactly the inverse transformation (inversion) for asking projection g (t, θ), is given to as θ
When, the one-dimensional Fourier transform of image projection Rg (t, θ) is equal to the two-dimensional Fourier transform to image g (x, y)；
One-dimensional Fourier transform is done to image projection first,
Two-dimensional Fourier transform is done again,
At this time by observation b (t, θ) anti-f (x, y) released be it is corrected after information.
Further, the determination method of the position of above-mentioned unknown medium 2, geometry and absorptivity and unknown medium 1
The theoretical solution procedure of relevant information is consistent, be mutually distinguishable only data after gain are different accordingly.
Further, the specific method is as follows for the error analysis and stability analysis of above-mentioned CT system: in the rotation of CT system
Turn in the case of number is limited, image reconstruction be it is ill posed, problem is constrained using the prior information of testee,
The approximate solution of former problem can be found out, regularization algorithm is just a process that；
The solution procedure of regularization method are as follows: when being solved to linear algebraic equation systems Ag=b, this problem can be turned
Turn to calculating | | Ag-b | |2Minimum, but the solution for ill-posed problem can add a penalty term, at this time former problem
Become:
Wherein, ψ (g) is taken as regular function,For the penalty term factor being attached on regular function, minimum is asked
Solution namely solves formula optimal solution；
According to geometrical relationship, the distance between sensing point member can be calculated,
When slope is definite value, x1/x2It also is certain value, it is possible thereby to which the coefficient for calculating r is (x1+1/x2), because of r
And x1/x2It substitutes into and calculates apart from relatively small, it is possible thereby to judge that influence of the small radius of circle to stability is smaller.
Compared with prior art, beneficial effects of the present invention:
1. the present invention is passed through the corresponding relationship of the projection of object by the increase and decrease and ray of dampening information, discriminate is utilized
Method, geometric method, perpendicular bisector method, which are established, rotates angle model about the CT system of slope and intercept, from the angle of Optimized model
Data are corrected processing by the precision for improving parameter, are carried out at Wavelet Denoising Method using the wdencmp function that MATLAB is carried
Reason, obtains CT image, and image quality is high；
2. the model that the present invention establishes has solved the parameters of CT system using method of geometry, intuitive and easy to understand；Meanwhile
When calculating the rotation center of CT system, the calculated parameter of the data randomly selected has reached certain precision, and data volume is not
Greatly, calculating is relatively easy, is the method for seeking approximate solution well.
Detailed description of the invention
Fig. 1 is CT system schematic diagram of the present invention.
Fig. 2 is template schematic diagram of the present invention.
Fig. 3 is 10 position views of the invention.
Fig. 4 is the perspective view of CT imaging of the present invention.
Fig. 5 is that projection information of the present invention is not overlapped schematic diagram.
Fig. 6 is that projection information of the present invention is overlapped schematic diagram.
Fig. 7 be ray of the present invention be 0 when schematic diagram.
Fig. 8 is that projection information of the present invention is overlapped schematic diagram.
Fig. 9 is projection information example diagram of the present invention.
Figure 10 is the difference variation diagram of 180 adjacent angulars of the invention.
Figure 11 is perpendicular bisector method schematic diagram of the present invention.
Figure 12 is the CT image of the unknown medium 1 of the present invention.
Figure 13 is the CT image of the unknown medium 2 of the present invention.
Figure 14 is precision analysis example diagram of the present invention.
Figure 15 is fourth quadrant X-ray schematic diagram of the present invention.
Specific embodiment
Further detailed description is done to the present invention combined with specific embodiments below, but embodiments of the present invention are not limited to
This.
In order to solve the problems, such as that image quality existing in the prior art is not good enough, present embodiments provides one kind and be based on
The CT system parameter calibration and imaging method of random transformation ,-Figure 15, should be joined based on the CT system that random is converted referring to Fig.1
Number calibration and imaging method, comprising:
Problem 1, the calibrating template that two homogeneous solid media composition is placed on square pallet, the geological information of template
With absorptivity it is known that the geological information of template such as Fig. 2, according to the calibrating template and its receives information, solve in CT system rotation
Position, the spacing of detector cells and 180 directions of X-ray of the heart in square pallet；
The reception information for the unknown medium 1 that CT system obtains in problem 2, Utilizing question 1, the calibration ginseng in Utilizing question 1
Number, determine position, geometry and the absorptivity of the unknown medium 1 in square pallet, and provide Fig. 3 to 10 positions
Set the absorptivity at place；
The reception information for another unknown medium 2 that CT system obtains in problem 3, Utilizing question 1, unknown medium 2 are corresponding
Data file it is known that calibrating parameters in Utilizing question 1, provide position of the unknown medium 2 in square pallet, geometry
Shape and absorptivity, and provide Fig. 3 to 10 positions at absorptivity；
Problem 4, design new template establish corresponding peg model, to improve the stated accuracy and stability of former CT system.
The X-ray of the two dimension CT system is just through two media, and one is testing medium, the other is air.One side
Face, seldom, radiation attenuation degree is small for the decaying due to caused by air, therefore absorptivity is 0.On the other hand, due to this two
Dimension testing medium is uniform, so the absorptivity of each point is 1 on medium.The numerical value of this and the absorptivity of template every bit is symbol
It closes.The attenuation of transmitted intensity usually has close ties, but CT in this subject with by the thickness of substance, density, ingredient
System is two-dimensional, and testing medium even density with testing medium, therefore need to only consider the road that ray passes through in the medium
Decay caused by diameter.
For problem one, firstly, considering that, using short-axis direction as X-axis, long axis direction is Y-axis using elliptical center as origin
Plane right-angle coordinate is established, by the special straight line in ray, such as ellipse tangent line, simultaneous linear equation and elliptic equation, then
Certain quantitative relations that may be present in figure are found, straight slope is solved, 180 rotation angles can be found out.Secondly, asking
It untwists during gyration, has found out when directions of rays determines, elliptical tangential equation.When family's parallel lines is worn
When crossing an ellipse about origin symmetry, by the straight line of origin by the oval line segment longest cut.The reception information of template is
Under 180 directions, information received by 512 units of detector, the growth trend for substantially observing these information can be with
It solving, the maximum value in each column is likely corresponded to by elliptical center, the i.e. ray of origin, and when data are hindered by one section of zero
Having non-zero values again after is exactly to represent to have ray by the oval air part between circle in this direction.It is giving
When determining directions of rays, parallel lines and ellipse have and only two tangent lines, the distance between this two tangent lines be also it is computable,
It can find out how many detector cells accounted among two tangent lines further according to the reception information of template, since detector cells are equidistant
Arrangement, thus the distance between tangent line and the ratio of corresponding detector cells sum as required by detector cells between spacing.
No matter directions of rays is how finally, CT system rotates how many angle, what is certain is that, rotation center one is scheduled on detector institute
On the perpendicular bisector of line segment, two not parallel straight lines determine an intersection point, therefore can be by appointing in the reception information of template
The data for taking 2 directions find out the coordinate of rotation center G with perpendicular bisector method.
For problem two, in the calibrated situation of CT system parameter, the unknown medium 1 that CT system obtains how is determined
In other words receiving the information such as position, geometry and absorptivity of the corresponding unknown medium of information in square pallet is exactly
When known observation, the problem of how determining Template Information in above-mentioned CT system.It is always deposited when initially being installed due to CT system
In error, and the reception information of actual measurement out is the gain process by CT system, it is therefore desirable to carry out school to observation
Just, it will obtain required Template Information by the reconstruction image of Radon transform using the data after correction and receive information.
For problem three, as the content of solution needed for problem two, the difference is that testing medium is different, the number received
According to also different.The process of replication problem two should can solve the unknown medium relevant information and Fig. 3 to 10 positions at
Absorptivity.
For problem four, to improve the precision of CT system imaging, substantially there are three aspects, increase the intensive journey of ray
Degree, whether model is optimal, corrects the parameter of CT system.Since the probe unit number of the two dimension CT system is definite value 512, and it is each
Probe unit equidistant arrangement, thus the concentration of ray be it is determining, can not change, consider from being optimized to model
Angle is set out, and finds out the best fit approximation solution of model to reduce error.The essence of regularization method be added some prior informations into
Row constraint, obtains the approximate solution of former problem.
Model hypothesis: assuming that X-ray is single energy；The decaying very little of the transmitted intensity as caused by air；Around not considering
The radiation interference of environment；The radiation that test substance itself generates is not considered；Test substance is respectively standard ellipse and standard round.
One, the specific method is as follows for the parameter calibration of CT system:
When testee is uniform dielectric, the transmitted intensity across object is exponentially decayed, it then follows
Lambert-beer law, being formulated out is exactly w=w0e-αl；
And on the path that ray only passes through air, the intensity of X-ray is almost unchanged, and therefore, the value of air is almost
It is zero；
In x-y plane, if the distribution function of attenuation coefficient is p (x, y), in the ray where l on the direction of straight line
Strength Changes are
After taking negative logarithm, it is denoted as f, physical quantity can be surveyed by being one, its physical significance is substance under the energy-ray
Line integral of the attenuation coefficient on the direction straight line l,
∫lP (x, y) dl=α ln (w/w0)
Due to homogeneous media in this subject, distribution function p (x, y) permanent is definite value.Observation given data only has 0,1 two kinds
Numerical value, therefore the definite value is 1.
1) the rotation angle model one of CT system
The direction for determining X-ray is taken as shown in Figure 1, the variation for receiving information of receiver is considered by diagram direction, with l's
Increase, dampening information increases to peak value by zero, then reduces, and ray passes through the oval gap with circle if it exists, i.e. ray extends only through
Air, then dampening information is reduced to zero on the basis of before, and zero may be kept constant on one section of section, until connecing down
The ray of the detector cells transmitting come just starts to gradually increase, when a certain ray is by the center of circle, reaches one again by circle
A peak value is then kept to zero, and edge is still zero just through the ray attenuation of air.
By taking Fig. 9 as an example, plane right-angle coordinate is established, wherein straight line AC is oval tangent line, and straight line OD is by ellipse
The heart, straight line BE is by the center of circle, it is assumed that AC between OD at a distance from be x1, OD between BE at a distance from be x2.If the linear equation of AC is y
=k (x+a), by docking the analysis for breath of collecting mail above, it can be found that x1With x2Ratio be figure in x3With x4Ratio, then by
Simple geometrical relationship is known
Observation Fig. 9 obtains elliptical center and center of circle distance OB, and x3And x4Ratio can be determined by the reception information of template,
So as to seek A0Length, and then find out the transversal away from a of straight line1。
Fig. 5 and Fig. 9 is symmetrical situation
Fig. 6 and Fig. 8 is also symmetrical situation, and method of geometry when referring to analysis chart 8, the similar triangles only chosen are not
Equally, the theorem proportional using similar triangles corresponding sides, obtaining the transversal proportionate relationship away from satisfaction of Fig. 5, Fig. 7 is
Since directions of rays is parallel with X-direction in Fig. 7, so slope is 0.
In above each situation it is transversal away from bring into linear equation and with elliptic equation simultaneous solution straight slope.
Y=k (x+a1)
Arrangement can obtain
(a2+a2k2)x2+2a2k2a1x+a2k2a1 2-a2b2=0
The direction of rotation model of CT system is established using discriminant method
Δ=2a2k2a1-4(a2+a2k2)(a2k2a1 2-a2b2)=0 (4)
The long axial length a=15 and the long b=40 of short axle that elliptic equation can be found out by the information of Fig. 2, by a, b and (3) formula are asked
The a solved1(4) formula of substitution can find out straight slope, and straight slope is the tangent value of the angle of straight line and X-axis positive direction,
It is programmed using MATLAB and acquires each straight slope and rotation angle (see annex program 1), the initial value for finding out rotation angle is
60.3664 degree, the rotation angle under 180 directions acquired is shown in annex table 1.
2) the detector cells spacing model two of CT system
Elliptical another tangent line determine need its it is transversal away from value, k is known at this time, observation (4) formula be about
It is transversal away from quadratic equation with one unknown, equation can solve.When the algebraic equation of two parallel lines all determines, between the two
Distance is represented by
Wherein a2Indicate another tangent line it is transversal away from, since ray is one group of parallel lines perpendicular to detector plane,
Therefore the d acquired is the sum of the length by the corresponding all detector cells of elliptical ray path.d0It is required detection
The spacing of device unit, n are the corresponding detector cells number of d, and the detector cells spacing model two for obtaining CT system is as follows
Five seed type as above is splitted data into using MATLAB, according to the algorithm idea of step as above, the result that will be acquired
It is averaged to obtain spacing to be 0.2753.
3) the rotation center model three of CT system
As shown in figure 11, straight line a and straight line b is respectively under detector direction 1, detector direction 2, perpendicular to detection
The perpendicular bisector of device plane, straight line c cross origin, since ellipse is about origin symmetry, so straight line c being equidistant to straight line a, b.
By observing the data of the reception information of template, corresponding detector cells sum between straight line b, c can be found out, due to spacing
Through calculating, therefore the length of the distance between b, c and entire detector can be found out.The distance between straight line b, c are
Wherein b0For total intercept of straight line b, since the slope of all directions has been found out, thus may determine that straight line b out
Slope-intercept form, the equation of straight line a, two linear equations of simultaneous can be found out with same method
Substitution is calculated transversal away from the intersection point that can solve two perpendicular bisectors by (5)
Point (x0,y0) it is exactly the position for needing to acquire the position of rotation center in the case where illustrating coordinate system.
In order to avoid contingency, the corresponding directions of rays of 5 column datas in the reception information of random modulus plate, directions of rays
Corresponding slope has been found out, match two-by-two the coordinate acquired be averaged to obtain rotation center coordinate be (- 9.4014,
6.1567)。
Two, the determination method of the position of unknown medium 1, geometry and absorptivity is as follows:
CT, which is imaged, is equivalent to the projection value Rg (t, θ) detected to all, the function g (x, y) of reverse attenuation coefficient,
This refutation process can be realized by Radon transform；
The parametric form definition of Radon transform is
Wherein g (x, y) function any straight line xcos θ+ysin θ=t in plane can be accumulated.Above formula is known as function g
The Radon transform of (x, y) is remembered b (t, θ)=Rg (t, θ)；
The gain coefficient of CT system is first found out, gain then is carried out to data
Wherein α=ln [(l0- l) l], calculate α=1.75；
Since the rotation center of CT system is not or not the center of square pallet, it is therefore desirable to do translation variation ability to data
Restore the raw information of data；
If rotation center is (a, b), following translation variation is done
R ρ (t, θ)=Rf (t-acos θ-bsin θ, θ)
Known by Central slice theorem, image reconstruction is exactly the inverse transformation (inversion) for asking projection g (t, θ), is given to as θ
When, the one-dimensional Fourier transform of image projection Rg (t, θ) is equal to the two-dimensional Fourier transform to image g (x, y)；
One-dimensional Fourier transform is done to image projection first
Two-dimensional Fourier transform is done again
At this time by observation b (t, θ) anti-f (x, y) released be it is corrected after information.
The absorptivity for calculating 10 points in Fig. 3 (see annex program 2) by MATLAB programming is respectively as follows: 0.0001,
0.0001.0.0003,0.0001,0.0002,0.0001,0.0001,0.0002,0.0004,1.000, the image of presentation is as schemed
12。
Three, the determination method of the relevant information of unknown medium 2 is as follows:
The theory of the relevant information of the determination method and unknown medium 1 of the position of unknown medium 2, geometry and absorptivity
Solution procedure is consistent, be mutually distinguishable only data after gain are different accordingly.The function carried using MATALB
Wdencmp function carries out Wavelet Denoising Method, and the image for reconstructing unknown materials 2 is as shown in figure 13.10 points in the Fig. 3 acquired
Absorptivity be respectively 0.0001,0.0001,1.0000,1.0000,0.5004,1.0000,1.0000,1.0000,
0.0500,1.0000.
Four, the specific method is as follows for the error analysis and stability analysis of CT system:
When the number of revolutions of CT system is limited, image reconstruction be it is ill posed, utilize the elder generation of testee
It tests information to constrain problem, the approximate solution of former problem can be found out, regularization algorithm is just a process that；
The solution procedure of regularization method is that can turn this problem when solving to linear algebraic equation systems Ag=b
Turn to calculating | | Ag-b | |2Minimum, but the solution for ill-posed problem can add a penalty term, at this time former problem
Become:
Wherein, ψ (g) is taken as regular function,For the penalty term factor being attached on regular function, minimum is asked
Solution namely solves formula optimal solution；
Regularization method belongs to one kind of least square method for essence:
Since the parameter of above-mentioned CT system provides to be built upon data are regarded as continuous image, point A is considered as a column
The maximum value of data, but due to data be it is discrete, the maximum value in the column data is not necessarily exactly the value at A, if with A institute
Value corresponding data in maximum value calculation, then solved in problem one with perpendicular bisector method, the equation of perpendicular bisector carries mistake
Difference.
Nonlinear fitting is carried out to the reception information of template by the nlinfit function of MATLAB, the transverse and longitudinal for finding out point A is sat
Mark can reduce error caused by this method instead of the abscissa acquired originally by the increase and decrease of data with the abscissa of A.
The distance between the bisector of perpendicular bisector and oval two tangent lines is
Thus the intercept of straight line is found out, and slope is it is known that the coordinate of the rotation center acquired still meets
It is 7.3300 using the abscissa that perpendicular bisector method finds out rotation center, error 0.224.
Enter on stability below, small radius of circle is adjusted the distance the influence of stability.According to geometrical relationship, can calculate
The distance between sensing point member
When slope is definite value, x1/x2It also is certain value, it is possible thereby to which the coefficient for calculating r is (x1+1/x2), because of r
And x1/x2It substitutes into and calculates apart from relatively small, it is possible thereby to judge that influence of the small radius of circle to stability is smaller.
Symbol description:
Annex
Table 1
Program 1
A=[304 302 301 301 298 296 295 294 292 291 291 288 287 286 285 284
282 282 281 280 279 278 278 277 277 276 276 276 276 276 276 277 277 278 278
279 280 281 282 283 284 285 287 288 290 292 293 295 297 299 301 303 305 307
309 311 313 315 317 319 322]；
B=[219 216 216 216 216 216 217 217 217 217 217 217 217 218 218 218
218 218 219 219 219 219 220 220 220 221 221 221 222 222 222 223 223 224 224
225 225 225 227 226 227 227 228 228 229 229 230 230 231 231 232 233 233 234
234 235 236 236 237 237 238]；
C=[77 76 74 73 72 71 70 69 67 67 66 65 63 63 63 62 61 61 60 60 60 60
59 59 59 59 59 59 59 60 60 60 61 61 62 62 63 64 64 65 66 67 68 69 70 71 73 74
75 77 78 79 81 83 84 86 88 90 91 93 95]；
X1=abs (b-a)；
X2=abs (c-b)；
x1/x2；
K=-40./sqrt ((45.*x1./x2) .^2-225)；%X ray slope
K=atan (k)；% calculates radian
K.*180./pi% calculates angle
M=45.*x1./x2%y=k (x+M) % calculates the λ value of the ray in figure, i.e. the distance between two rays (M
+45).*k./sqrt(k.^2+1)
Data
A=[304 302 301 301 298 296 295 294 292 291 291 288 287 286 285 284
282 282 281 280 279 278 278 277 277 276 276 276 276 276 276 277 277 278 278
279 280 281 282 283 284 285 287 288 290 292 293 295 297 299 301 303 305 307
309 311 313 315 317 319 322]；
B=[219 216 216 216 216 216 217 217 217 217 217 217 217 218 218 218
218 218 219 219 219 219 220 220 220 221 221 221 222 222 222 223 223 224 224
225 225 225 227 226 227 227 228 228 229 229 230 230 231 231 232 233 233 234
234 235 236 236 237 237 238]；
C=[77 76 74 73 72 71 70 69 67 67 66 65 63 63 63 62 61 61 60 60 60 60
59 59 59 59 59 59 59 60 60 60 61 61 62 62 63 64 64 65 66 67 68 69 70 71 73 74
75 77 78 79 81 83 84 86 88 90 91 93 95]；
x1./x2
Vpa(k)
A-M
K=40./sqrt ((45.*x1./x2) .^2-225)
A=[188 185 184 182 179 177 175 173 171 168 166 164 162]；
B=[274 274 273 272 272 271 270.5 270 269 268 268 267 266]；
C=[416 413 412 409 407 405 403 400 398 395 393 391 388]；
N-BH
K=40./sqrt ((45+45.* (x1-x2) ./x2) .^2-225)
A=[160 157 155 153 151 149 147 145 143 141 139 137 135 133 131 129
127 126 124 122 120 119 117 116 114 113 111 110 108 107 105 104 103 102 100
99 98 97 96 95 94 93 93 92 91 90 90]；
B=[266 265 264 264 263 262 262 261 260 259.5 259 258 257 257 256 255
255 254 253 252 252 251 250 250 249 248 248 247 246 246 246 244 243.5 243 242
241.5 241 240 240 239 238 238 238 234 231 227 224]；
C=[385 383 380 377 363 361 359 357 354 352 350 347 345 342 339 337
334 331 329 325 324 319 316 313 310 307 304 301 298 295 291 288 285 282 278
275 272 268 265 262 258 255 252 248 245 242 238]；BI
BJ-DF
K=-40./sqrt ((45+45.* (x1-x2) ./x2) .^2-225)
A=[378 378 377 377 376 375 374 374 373 372 371 370 369 368 367 366
365 364 363 362 361 359 358 357 356 354 353 352 351 349 348 346 345 344 342
341 339 338 336 335 333 332 330 329 327 325 324 322 321]；
B=[246 243 240 236 233 231 230 230 229 229 228 228 227 227 226 226
225 225 224 224 223 223 223 222 222 222 221 221 221 220 220 220 219 219 219
219 218 218 218 218 218 217 217 217 217 217 217 216 216]；
C=[232 228 225 222 219 215 212 209 206 202 199 196 193 190 187 184
181 178 175 172 169 166 163 160 158 155 152 150 147 145 142 140 137 135 133
131 129 127 125 123 121 119 118 116 115 113 112 96 94]；
DG-FX
K=-40./sqrt ((45.*x1./x2) .^2-225)
A=[319 318 316 314 313 311 310 308 306 305 303 302 300 299 296 295
294 292 291 291 288 287 286 285 284 282 282 281 280 279 278 278 277 277 276
276 276 276276 276 277 277 278 278 279 280 281 282 283 284 285 287 288 290
292 293 295 297 299 301 303 305 307 309 311 313 315 317 319 322]；
B=[216 216 216 216 216 216 216 216 216 216 216 216 216 216 216 217
217 217 217 217 217 217 218 218 218 218 218 219 219 219 219 220 220 220 221
221 221 222 222 222 223 223 224 224 225 225 225 227 226 227 227 228 228 229
229 230 230 231 231 232 233 233 234 234 235 236 236 237 237 238]；
C=[92 91 89 87 85 83 82 80 79 77 76 74 73 72 71 70 69 67 67 66 65 63
63 63 62 61 61 60 60 60 60 59 59 59 59 59 59 59 60 60 60 61 61 62 62 63 64 64
65 66 67 68 69 70 71 73 74 75 77 78 79 81 83 84 86 88 90 91 93 95]；
Program 2
D=0.2768；
Xc=-33.5*d；
Yc=20*d；Position of the % rotation center on pallet
Phantom=A；
Phantom=[zeros (100,180)；phantom；zeros(100,180)]；
Img=iradon (phantom, [0:179]+30) % acquires absorptivity by Radon transform
N=size (img, 1)；
[x, y]=meshgrid ([- n/2:n/2] * d)；%100/256imagesc (x (1 :), y (:, 1), img) % weight
Build video
Colormap (gray) % gray scale
holdon
line([-50 50],[-50 -50],'color','w')
line([-50 50],[50 50],'color','w')
line([50 50],[-50 50],'color','w')
Line ([- 50-50], [- 50 50], ' color', ' w') % tray position
holdon
plot(xc,yc,'ok')
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, exist
Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention
Protection scope.
Claims (5)
1. a kind of CT system parameter calibration and imaging method based on random transformation, it is characterised in that: include:
Problem 1, the calibrating template that two homogeneous solid media composition is placed on square pallet, the geological information of template and suction
Yield solves position of the CT system rotation center in square pallet, visits it is known that according to the calibrating template and its receive information
Survey the spacing of device unit and 180 directions of X-ray；
The reception information for the unknown medium 1 that CT system obtains in problem 2, Utilizing question 1, the corresponding data file of unknown medium 1
It is known that the calibrating parameters in Utilizing question 1, determine position, geometry and the absorption of the unknown medium 1 in square pallet
Rate；
The reception information for another unknown medium 2 that CT system obtains in problem 3, Utilizing question 1, unknown medium 2 count accordingly
According to file it is known that calibrating parameters in Utilizing question 1, position of the unknown medium 2 in square pallet, geometry are provided
And absorptivity；
Problem 4, design new template establish corresponding peg model, to improve the stated accuracy and stability of CT system.
2. CT system parameter calibration according to claim 1 and imaging method, which is characterized in that the parameter of the CT system
The specific method is as follows for calibration:
When testee is uniform dielectric, the transmitted intensity across object is exponentially decayed, it then follows Lambert-
Beer law, being formulated out is exactly w=w0e-αl；
And on the path that ray only passes through air, the intensity of X-ray is almost unchanged, and therefore, the value of air is almost nil；
In x-y plane, if the distribution function of attenuation coefficient is p (x, y), in the transmitted intensity where l on the direction of straight line
Variation is
After taking negative logarithm, it is denoted as f, physical quantity can be surveyed by being one, its physical significance is decaying of the substance under the energy-ray
Line integral of the coefficient on the direction straight line l,
∫lP (x, y) dl=α ln (w/w0)
Due to homogeneous media in this subject, distribution function p (x, y) permanent is definite value.
3. CT system parameter calibration according to claim 1 and imaging method, which is characterized in that the unknown medium 1
The determination method of position, geometry and absorptivity is as follows:
CT, which is imaged, is equivalent to the projection value Rg (t, θ) detected to all, the function g (x, y) of reverse attenuation coefficient, this
Refutation process can be realized by Radon transform；
The parametric form definition of Radon transform is,
Wherein g (x, y) function any straight line xcos θ+ysin θ=t in plane can be accumulated, and above formula is known as function g's (x, y)
Radon transform is remembered b (t, θ)=Rg (t, θ)；
The gain coefficient of CT system is first found out, gain then is carried out to data,
Wherein α=ln [(l0- l) l], calculate α=1.75；
Since the rotation center of CT system is not or not the center of square pallet, it is therefore desirable to which doing translation variation to data could restore
The raw information of data；
If rotation center is (a, b), following translation variation is done,
R ρ (t, θ)=Rf (t-acos θ-bsin θ, θ)
To be known by Central slice theorem, image reconstruction is exactly the inverse transformation (inversion) for asking projection g (t, θ), timing is given to as θ,
The one-dimensional Fourier transform of image projection Rg (t, θ) is equal to the two-dimensional Fourier transform to image g (x, y)；
One-dimensional Fourier transform is done to image projection first,
Two-dimensional Fourier transform is done again,
At this time by observation b (t, θ) anti-f (x, y) released be it is corrected after information.
4. CT system parameter calibration according to claim 1 and imaging method, which is characterized in that the unknown medium 2
The determination method of position, geometry and absorptivity is consistent with the theoretical solution procedure of relevant information of unknown medium 1, mutual area
It is other that only the data after gain are different accordingly.
5. CT system parameter calibration according to claim 1 and imaging method, which is characterized in that the error of the CT system
The specific method is as follows with stability analysis for analysis:
When the number of revolutions of CT system is limited, image reconstruction be it is ill posed, utilize testee priori letter
Breath constrains problem, can find out the approximate solution of former problem, regularization algorithm is just a process that；
The solution procedure of regularization method are as follows:
When solving to linear algebraic equation systems Ag=b, this problem can be converted to calculating | | Ag-b | |2Minimum, but
Solution for ill-posed problem can add a penalty term, and former problem becomes at this time:
Wherein, ψ (g) is taken as regular function,For the penalty term factor being attached on regular function, minimum is solved
Exactly formula optimal solution is solved；
According to geometrical relationship, the distance between sensing point member can be calculated,
When slope is definite value, x1/x2It also is certain value, it is possible thereby to which the coefficient for calculating r is (x1+1/x2), because of r and x1/
x2It substitutes into and calculates apart from relatively small, it is possible thereby to judge that influence of the small radius of circle to stability is smaller.
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| CN109682843A (en) * | 2019-02-13 | 2019-04-26 | 重庆交通大学 | A kind of parameter calibration method of pair of CT system |
| CN110243847A (en) * | 2019-07-04 | 2019-09-17 | 湖南理工学院 | A kind of CT system parameter calibration and imaging method |
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| CN109682843A (en) * | 2019-02-13 | 2019-04-26 | 重庆交通大学 | A kind of parameter calibration method of pair of CT system |
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